2.1 The tropical atmosphere
2.2 Regional climatology
2.3 Measurement of point rainfall
2.4 Estimation of areal rainfall
2.5 Frequency distribution of annual, monthly and daily rainfall
2.6 Frequency distribution of extreme values
2.7 Rainfall intensity, duration and frequency
2.8 Occult precipitation
Tropical Africa can be defined geographically as the area of the continent lying between the Tropics of Cancer and Capricorn, or, meteorologically, as the area of Africa where the weather sequences and climate differ distinctly from those in middle and high latitudes (Lockwood, 1972).
In this zone, the effects of the spinning earth are least marked and with the exception of the east coast, widespread uniformity of temperature and humidity gives the nearest approach to the classical model of the general circulation of the atmosphere, the Hadley cell.
This model is shown schematically in Figure 1. In the simplest terms, one can consider the atmosphere as a gigantic heat engine, driven by solar radiation, and modified by the earth's rotation. Solar radiation provides the energy source for evaporation and for heating the earth's surface.
Figure 1. Diagrammatic representation of the Hadley cell and meridional circulation.
The equatorial regions receive more incoming radiation than they lose through longwave radiation. This surfeit of net radiation at the equator is balanced by a radiation deficit towards the poles. The temperature gradient which builds up between equator and poles drives the general circulation of the atmosphere and, in the absence of rotation, would lead to a poleward flow of warm air in the upper troposphere and a compensating return flow towards the equator at surface levels.
Because of the earth's rotation, a discontinuity in the poleward flow exists around latitudes 30°S and 30°N. Here the increasing effect of the earth's rotation produces a belt of high wind speeds directed towards the west, known as jet streams. These increases in wind speed in the upper levels of the atmosphere place a limit on the upper poleward flows.
To add further to the complexity of the picture, waves exist in the upper atmosphere in middle latitudes. These are associated with the boundary between polar and tropical air. An eastwards flowing jet stream is a feature of these waves; occasionally this stream is displaced to the lower latitudes. This displacement is particularly pronounced when the sun is overhead in either the northern or southern tropics.
Satellite studies have revealed, however, a much more complex pattern of atmospheric circulation over land areas within the tropics than the above comments suggest (Barrett, 1974). Theoretical studies have also demonstrated that more complex patterns of equatorial cells can exist (Asnani, 1968).
Nevertheless, the simple model is useful in explaining the existence of the major deserts. Subsidence of air from the Hadley cell rotation in subtropical regions makes it almost impossible for clouds to form, and thus for the rain-making process to be initiated. The Sahara and Kalahari deserts, therefore, are the result of atmospheric subsidence and are not due to a lack of atmospheric moisture.
The simple model also explains the existence of the trade winds. These are prevailing winds flowing from the subtropical anticyclones towards the equator. The southeast and northeast trade winds flow towards the zone of relatively low pressure in the region of the equator. According to Findlater (1971) two troughs exist, often separated by a westerly counterflow. This counterflow can be an important feature in bringing moist maritime air to the western side of the continent.
Although the stream of relatively cool maritime air associated with the trade winds is capable of bringing rain, the flow is often divergent, and the presence of a trade wind inversion suppresses any convectional growth. The altitude of the inversion rises towards the equator as the broad-scale subsidence weakens, and the equatorial zone becomes a zone of convergence where towering cumulous clouds can develop.
This zone is often termed the 'intertropical convergence zone' (ITCZ), and the migration north and south of the equatorial troughs associated with the ITCZ, following the apparent movement of the sun, is one of the most important climatic factors in Africa. The ITCZ is not a zone of rainfall. It is a zone of instability within which a number of factors can lead to a triggering of the rainfall mechanism. Often the zone is difficult to identify, or it may be split into a series of zones within the equatorial troughs. Because of the relatively uniform pressure and temperature, small pressure gradients often modify the flow pattern on the surface of continents in the equatorial regions. The interaction between the flows and topographic barriers (such as the highlands of East Africa) and large lakes (such as those in the Great Rift Valley) gives rise to local forced convection and to heavy rainfall.
The release of latent heat by condensing water vapour may trigger a series of violent thunderstorms over a wide area, even though the build-up of the critically unstable layer may take several days. Much of the rainfall in the tropical regions is of this type. Recent satellite imagery has confirmed the presence of cloud clusters - concentrations of cumulous clouds in linear arrays or in irregular clusters, separated by clear areas of weak subsidence. Unfortunately, the origin and mechanism of such features, which were formerly much more difficult to observe let alone study, is still not fully understood. Thus, in a region where the onset and duration of rainfall is critical to man, prediction and forecasting of rainfall are still in their infancy.
Our understanding of the dynamic atmosphere within the tropics is imperfect. However, the movements of the equatorial troughs is an important and significant feature which helps to identify the area within which rainfall is most likely to occur. The controls on the movement of the troughs are partly extratropical and arise from the energy exchange between the equator and the poles. Clearly, the strength and position of the subtropical high-pressure systems are critical and determining how far north and south of the equator the equatorial troughs move.
The devastating droughts in the Sahel region of West Africa during 1972 can be explained in terms of anomalous easterly flow patterns over western Arabia and Africa between the equator and 20°N (Krueger and Winston, 1975). This easterly flow inhibited the growth of the normal westerly flow and has been shown by Minja (1982) to have arisen from anticyclones centred over North Africa and Egypt. Mean flow patterns show that anticyclones are usually confined to the North African coast and are very much weaker than those which occurred in 1972. This example is given to show that an understanding of dynamic climatology assists in explaining much of the deviation from the statistical means on which most regional climatological studies are based.
Many subjective attempts have been made to classify regional climates e.g. Herbertson (1905), Koppen and Geiger (1954), Pollock (1968) and Griffiths (1972). All suffer from trying to portray a dynamic system in a static sense. More recent works acknowledge this difficulty and attempt to describe the mechanisms or controls on the seasonal changes in pressure, temperature, rainfall and wind patterns (Lockwood, 1972).
There is still a need, however, to present the mean patterns, and the arithmetic mean values of meteorological variables are the climatic indices most readily available. Climatic classifications based on such statistics, although useful for broad comparisons, may produce a misleading picture of 'fluid continuum subject to kaleidoscopic variations in its form' (Barrett, 1974).
For example, the mean annual rainfall, at a particular station, is expected to be equalled or exceeded 50% of the time. Rainfall is expected also to be less than or equal to the mean for the other 50% of the time. For both agriculturalists and pastoralists the risk factor in accepting mean annual rainfall as a design parameter is too high, and far more appropriate indices are the rainfall amounts with an 80 or 90% probability of occurrence. These can be found from an analysis of the frequency distribution of annual rainfall. They are values which, on average, will not be reached in 1 year out of 5 (80%), or 1 year out of 10 (90%).
Mean annual or mean monthly rainfalls, however, are valuable statistics in their own right, often being strongly correlated with other variables. Their presentation below is perfectly justified as long as the limitations of arithmetic means are fully understood.
Acknowledging that classifications of climate based solely on mean statistics are of limited value to the user, it becomes apparent that the purpose to which a classification is to be put becomes the most important criterion in any 'genetic' classification. In terms of water resources, precipitation is the most important climatic variable, and it is well known that its temporal and spatial variability will determine the range of human activities which are possible in practice. In seeking to evaluate both this range of activities within certain areas and the constraints or factors limiting these activities, it is useful therefore as a starting point to take the mean patterns of seasonal rainfall over tropical Africa. These patterns are closely related to the mean positions of the equatorial troughs, and anomalies in rainfall distribution can frequently be related to significant changes in the position of the troughs in particular years.
Thompson (1965) gives mean monthly rainfall patterns in a series of 12 maps of which four are reproduced here (Figures 2 to 5). These demonstrate clearly how the equatorial troughs migrate north and south bringing rainfall to different parts of Africa.
In January (Figure 2), the main areas of precipitation are in a zone centred between latitudes 10°S and 15°S, with maxima on the eastern side of the continent. This pattern corresponds well with the penetration south of the equator of the northeast monsoon in the Indian Ocean (Findlater, 1971), bringing the heaviest rainfall to Madagascar and the eastern continental margins. It is also during January when tropical cyclones develop in the southern Indian Ocean bringing, on average, two storms of hurricane intensity a year. The steep topography of the island of Madagascar helps to promote some of the most intense and heavy falls of rain (Barrett, 1974). Occasionally, these storms penetrate the Zambezi Valley and Mozambique and Malawi. Generally speaking, however, the frequency of tropical storms in this part of the Indian Ocean is very small compared to an average of 22 per year in the northwest Pacific Ocean, and about 10 per year in the northeast Pacific Ocean.
The dryness of the western side of the continent south of the equator is usually attributed to the dominance and persistence of the south Atlantic anticyclone, which gives rise to strong subsidence in the layers near the surface (Thompson, 1965).
By April (Figure 3), the troughs have moved far enough north to produce a zone of maximum rainfall astride the equator. Flow from the south Atlantic anticyclone towards troughs situated significantly further to the north in West Africa (between 10° and 15°N), brings rainfall to the West African coast as far south as Angola. In East Africa, the northeasterly flow across the northern Indian Ocean has been replaced by a strengthening southeasterly flow which penetrates as far inland as the East African highlands, bringing rainfall to a wide area. Strong flow develops first at low levels, then at higher levels, and a notable feature is the bifurcation of the core of the southern monsoon. One branch penetrates eastern Africa, while the other recurves between two well marked equatorial troughs into a westerly flow towards the southern tip of Sri Lanka.
As the troughs continue to move northwards, the circulating flow becomes most marked in July- (Figure 4). During this month, the northern equatorial trough is positioned along the south Arabian peninsula, whereas the southern equatorial trough is astride the equator. The core of highest wind speeds at the surface now runs from the northern tip of Madagascar in a northwesterly direction, turning north across the equator just off the East African coast, and curving northeastwards across the Indian Ocean, to become the well known southwest monsoon of the Indian subcontinent. As can be seen from Figure 4, only a very small area of the east coast receives rainfall, together with the eastern margins of Madagascar. In West Africa, however, the southwesterly flow between the two troughs has strengthened, producing the 'southwest monsoon' (Lambergeon, 1982), and bringing rainfall, in a zone between 0° and 10°N, across the continent as far east as Ethiopia.
Figure 2. Mean January rainfall in Africa.
In the months between July and September, the situation changes little except for a gradual movement south of the southern equatorial trough in West Africa. By October (Figure 5), the weakening of the subtropical pressure system over southern Africa allows a southward extension of the convergence in central Africa. In East Africa, the northern equatorial trough moves over Ethiopia and Somalia and, once again, the westward penetration of the southeasterly monsoon current brings rainfall to coastal regions. Rainfall is also found in the southeastern part of the continent as a weak flow of the southeasterly monsoon swings south of Madagascar. This pattern intensifies with the penetration of the north-east monsoon south of the equator in November and December, until the January stage is reached again with strong convergence south of the equator on the eastern side of the continent, bringing widespread rainfall.
These illustrations of the seasonal movements of mean monthly rainfall are subject to the comments made previously about variability and reliability. Individual annual and seasonal distributions of rainfall can, and do, vary widely from the mean pattern. In addition local conditions, particularly in the vicinity of mountains, escarpments and large bodies of water, can produce deviations from the general picture.
An example of the reliability of rainfall within the overall seasonal pattern is shown in Figure 6, which gives the 4:1 confidence limits of peak date and seasonal quantity of rainfall for African stations between 8°N and 5°S (Manning, 1956). The relationship between peak rainfall and the apparent movement of the ITCZ is clear.
The seasonal and annual ranges of temperature, humidity and potential evaporation are much less pronounced, except that these variables exhibit strong and regular diurnal variations. From the point of view of water resources, potential evaporation is particularly important since it integrates the effects of all other variables including rainfall.
As progress is made towards an understanding of the mechanism and controls of the general circulation of the atmosphere, so the reliability of forecasts will increase. At the present time, however, it is not possible to forecast either the onset or the duration and intensity of tropical rainfall. However, it is possible to obtain reliable predictions of rainfall amounts where sufficient data exist for a statistical analysis of a series of events. This will indicate the average likelihood of an event occurring over a specified period. But it will not indicate when the event will occur, nor does it assist in predicting, for example, when there will be a series of dry years such as those which have characterised many of the major drought periods. This topic is dealt with in a later section.
Figure 3. Mean April rainfall in Africa.
Figure 4. Mean July rainfall in Africa.
Rainfall is most commonly measured daily at a fixed time in the morning, and the measured quantity, expressed as depth in millimetres, is attributed to the previous day. The 'standard' rain gauge varies in orifice diameter and height above the ground in different countries, but most have adopted the World Meteorological Organisation guidelines of a 150 to 200 cm2 collector area positioned 30 cm to 1 m above the ground. If rainfall occurs during the morning, and a rain gauge is read during a storm, the total quantity in that storm will be attributed to two separate days. This is an important factor to take into account when assessing the frequency of large falls of rain.
Another type of rain gauge is the recording, or autographic, gauge which traces amount of rainfall against time on a strip chart. Some newer gauges employ tipping buckets which record, via a magnetic switch, counts or tips in a digital form, on either solid-state or magnetic-tape loggers. These rain gauges are used to analyse the intensity of rainfall and are particularly useful in assessing storm profiles, infiltration rates, surface runoff or rainfall erosivity.
Storage gauges are rain gauges which are left in remote areas for periods of time between visits ranging from 1 week to 1 month. Where evaporation is high, oil can be used to inhibit losses. Calibrated dipsticks are used to measure rainfall between visits. Once again, small solid-state recorders make it possible for storage gauges to be measured at infrequent intervals to give daily rainfalls. The usefulness of all rain gauges is limited by the effectiveness of protection against vandalism.
Figure 5. Mean October rainfall in Africa.
Radar has been used with some success to measure rainfall in cases where high costs can be justified in order to obtain real time data, as in the case of flood forecasting. Radar has also been used to detect hail formation in the tea-growing area of Kericho in Kenya. Clouds can be seeded to curtail the growth of large hailstones, which can cause costly damage to a high-value cash crop.
With the ever increasing quality of satellite imagery it is possible to correlate cloud type, density and thickness with rainfall, using 'ground truth' stations. Once again the cost of such a computer-based exercise has to be weighed against the value of the rainfall data.
Telemetering of rainfall information has been developed in certain remote areas to minimise the transport costs of gathering rainfall data. This, and other remote or automated techniques (including the use of automatic weather stations), is not likely to replace the widespread system of volunteer observers using simple standard rain gauges until realistic monetary values can be placed on sets of reliable rainfall data. However, as technological advances reduce capital installation costs, and as fuel prices continue to rise, the gap between manual and automated systems in terms of total costs may not be so great.
Rainfall over an area is usually estimated from a network of rain gauges. In theory, these gauges should either be placed in a random sampling array, or be set out in a regular or systematic pattern. A combination of sampling techniques, as in a stratified random sampling network, is often used to increase the efficiency of sampling i.e. to decrease the number of gauges required to estimate the mean rainfall with a given precision (McCulloch, 1965).
In practice, gauges are usually placed near roads and permanent settlements for convenience of access, rather than according to a strict sampling array. There is a danger that bias can be introduced into the estimated mean areal rainfall. This was first pointed out by Thiessen (1911), who advocated the construction of Thiessen polygons to give a weighting inversely proportional to the density of rain gauges.
In mountainous areas, for example, fewer gauges tend to be placed in the inaccessible areas which often have the highest rainfall. Careful inspection is needed, therefore, to determine whether the mean is affected by serious bias, and whether this can be corrected using the Thiessen method.
The most rational way of estimating mean rainfall is by constructing isohyets (lines joining places of equal rainfall) on a map of the area in question. This takes into account such factors as the increase in rainfall with altitude on the windward side of hills and mountains, the rain shadow on the leeward side of hills and mountains and the aspect of topographic barriers in relation to prevailing winds. The assumption is made that rainfall is a continuous spatial variable i.e. if two rain gauges record 100 mm and 50 mm respectively, there must be some place between the two gauges which has received 75 mm. Glasspoole (1915) sets out some criteria for drawing isohyets for the British Isles which have general application.
Once the isohyets have been drawn, mean areal rainfall is calculated by computing the incremental volumes between each pair of isohyets, adding the incremental amounts and dividing by the total area.
Because of the labour involved in measuring the area between isohyets, several automated techniques have been devised. These include fitting various 'surfaces' to the rainfall data, calculating Thiessen polygon areas automatically or applying finite element techniques (Edwards, 1972; Shaw and Lynn, 1972; Lee et al, 1974; Chidley and Keys, 1970; Hutchinson and Walley, 1972). These techniques are basically designed to accommodate irregularly spaced rain gauges in areas where spatial variation is important, or to provide techniques which can readily be adapted to the computer processing of rainfall data.
In semi-arid areas, the temporal and spatial variability of rainfall is such that rainfall networks are rarely dense enough to reflect adequately either the mean or the variance of areal rainfall. Even where relatively dense networks (e.g. 1 gauge per 700 km2) are installed as part of research programmes (Edwards et al, 1979), there are difficulties in constructing isohyetal maps, and considerable changes in the seasonal pattern of rainfall can be discerned.
Generally speaking, random sampling networks give a better estimate of the variance of mean rainfall, and systematic sampling networks give a better (i.e. unbiased) estimate of the mean. In some cases, as in network design, the former is more important since it leads to estimates of the precision of the mean or, conversely, to determining the number of gauges necessary for estimating the mean with the required precision. For most general purposes, however, a systematic spatial coverage can be relied upon to give unbiased estimates of the mean.
In this context it is useful to distinguish between an estimate's precision i.e. its repeatability in a sampling sense, and its accuracy, which is a function of both the sampling technique and the estimate of 'true' rainfall at a point.
Rain gauges are of many different heights above the ground. Variations in the cross-sectional area of the gauge from its nominal value, which may be due to poor construction or damage, overexposure of gauges to high wind speeds across the orifice, shelter of the gauge by vegetation, and common observer mistakes, all contribute to inaccuracies in point rainfall measurements. Normally these are small compared to the seasonal and annual variability of rainfall but, in certain cases, these potential sources of error have to be taken into account. Such cases include the measurement of rainfall above forest canopies and in areas of high wind speed.
Agriculturalists and pastoralists require statements concerning the reliability of rainfall. A convenient means of making such statements is provided by confidence limits. These are defined as the estimates of the risk of obtaining values for a given statistic that lie outside prescribed limits (Manning, 1956). The limits commonly chosen are 9:1 and 4:1. With 9:1 limits a figure outside the limits is to be expected once in 10 occasions, and half of these occasions (i.e. one in 20) are to be expected below the lower limit and half above the upper limit. Thus the 9:1 lower confidence limit of annual rainfall would represent the level of rainfall which is expected not to be reached 1 year in 20. Similarly, the 4:1 lower confidence limit is expected not to be reached 1 year in 10.
In order to establish values for such limits, it is necessary to assume a theoretical frequency distribution to which the sample record of data can be said to apply. Manning (1956) assumed that the distribution of annual rainfall in Uganda was statistically normal. Jackson (1977) has stressed that annual rainfall distributions are markedly 'skew' in semi-arid areas and the assumption of a normal frequency distribution for such areas is inappropriate. Brooks and Carruthers (1953) make general statements that three-yearly rainfall totals are normally distributed, that annual rainfall is slightly skew, that monthly rainfall is positively skew and leptokurtic, and that daily rainfall is 'J' shaped, bounded at zero. They go on to suggest that empirical distributions be used, such as log-normal for monthly rainfall, and an exponential curve (or a similar one) fitted to cumulative frequencies for daily rainfall.
For annual rainfall series which exhibit slight skewness and kurtosis, Brooks and Carruthers suggest that adjusting the normal distribution is easier and more appropriate than using the Pearson system of frequency curves (Elderton, 1938; Fisher, 1922). As the degree of skewness and kurtosis increases, log-normal transformations should be used.
These comments apply equally well to tropical rainfall where annual totals exceed certain amounts. For example, Gregory (1969) suggests that normality is a reasonable assumption where the annual rainfall is more than 750 mm. On the other hand, Manning (1956) gives examples where the normal frequency distribution fits reasonably well to stations with less than 750 mm (Table 1). Kenworthy and Glover (1958) suggest that in Kenya normality can be assumed only for wet-season rainfall. Gommes and Houssiau (1982) state that rainfall distribution is markedly skew in most Tanzanian stations.
Inspection of the actual frequency distribution, at given stations, and simple tests for normality can quickly establish whether or not the normal distribution can be used. Such tests include the comparison of the number of events deviating from the mean by one, two or three standard deviations with the theoretical probability integral. If not, a suitable transformation must be chosen before confidence limits or the probabilities of receiving certain amounts of rainfall can be calculated.
Maps have been prepared for some regions, particularly East Africa (East African Meteorological Department, 1961; Gregory, 1969), showing the annual rainfall likely to be equalled or exceeded in 80% of years. These are extremely useful for planning purposes although, as Jackson (1977) points out, these refer to average occurrences over a long period of years. Statements such as 'the rainfall likely to be equalled or exceeded 4 years in 5' must be qualified by 'on average' to indicate that it does not rule out the occurrence of, say, 3 years of 'drought' rainfall in a row.
Table 1. Confidence limits of rainfall for some stations receiving less than 762 mm.
Station |
Annual mean (mm) |
No. of years of record |
4:1 limits |
Deviation |
||
lower |
upper |
actual |
expected |
|||
| Utusi, Uganda | 760 | 14 | 406 | 1118 | 4 | 2.8 |
| Sokota, N. Nigeria | 693 | 40 | 508 | 864 | 7 | 8.0 |
| Namanga, Swaziland | 661 | 35 | 381 | 940 | 6 | 7.0 |
| Chipinea, Zimbabwe | 653 | 23 | 406 | 889 | 4 | 4.6 |
| Kibaya, Tanzania | 643 | 12 | 330 | 940 | 2 | 2.4 |
| Maiduguri, N. Nigeria | 627 | 38 | 406 | 864 | 8 | 7.6 |
Source: Manning (1956).
When dealing with the frequency distribution of maxima or minima, it is necessary to use other empirical frequency distributions which give a more satisfactory fit to the observed data. There are no rigid rules governing which type of distribution is most appropriate to a particular case, and a variety of empirical frequency or probability distributions are available in standard statistical textbooks (Table 2). As a general guide, extremal distributions are concerned with the exact form of the 'tail' of the frequency distribution. Because such occurrences are rare events, it is unusual to have a sufficiently long record for the shape of the asymptotic part of the curve to be defined with any certainty. Brooks and Carruthers (1953), for example, feel that the Gumbel distribution (Gumbel, 1942), which is commonly used in flood frequency prediction, tends to underestimate the magnitude of the rarer rainfall events.
In most applications it is usual to linearise the distribution by calculating cumulative frequencies and then plotting on double logarithmic versus linear graph paper (extreme probability graph paper). If the actual distribution is close to the theoretical distribution postulated by Gumbel, the plotted points approximate to a straight line. An example of this is shown in Figure 7 which demonstrates how a cumulative distribution can be linearised by the use of special probability paper (Ven te Chow, 1964). The same author points out that the abscissae and ordinates are normally reversed to show the probabilities as abscissae. Figure 8 is an example of the more usual presentation of data plotted on extreme probability paper. In this case maximum daily rainfalls for June, in Lagos, closely fit the Gumbel distribution.
In this context it is useful to mention that most analyses of frequencies of rainfall or other hydrological events are expressed in terms of the recurrence interval of an event of given magnitude. The average interval of time, within which the magnitude of the event will be equalled or exceeded, is known as the recurrence interval, return period or frequency. It is common, therefore, to refer to the 10-year or the 100-year flood, or the 24-hour rainfall, for example.
The recurrence interval (N) should not be thought of as the actual time interval between events of similar magnitude. It means that in a long period, say 10 000 years, there will be 10 000/N events equal or greater than the N-year event. It is possible, but not very probable, that these events will occur in consecutive years (Linsley and Franzini, 1964).
Table 2. Common types of frequency distribution used for hydrological events.
Type |
Characteristics |
Example |
| 1. Binomial | Discrete events in two categories | Number of 'dry' months in each year |
| 2. Poisson | 'J' shaped distribution of discrete events possible number of occurrences very small | Frequency of heavy rainstorms |
| 3. Normal | Symmetrical, bell-shaped continuous distribution (Gaussian) | Annual rainfall in wet regions |
| 4. Adjusted normal | As for 'normal distribution' but slightly skew | Annual rainfall |
| 5. Log-normal | Positively skew and leptokurtic | Annual rainfall in semi-arid areas, monthly rainfall |
| 6. Pearson type I | Bounded both ends, bell or 'J'-shaped, skew | Monthly rainfall with very dry months |
| 7. Pearson type III | Bounded one end, bell or 'J'-shaped, skew (log-normal is a special case) | Frequencies of wind speed |
| 8. Extreme distribution type I | Asymptotic, unbounded (Gumbel) | Flood frequency, rainfall intensity/frequency |
| 9. Extreme distribution type III | Asymptotic, bounded at a minimum value | Drought frequency |
It is a general feature of rainfall, and one which is not necessarily confined to the tropics, that a small proportion of intense storms of short duration produce most of the total rainfall (Richl, 1954; 1956). Thus, 10 to 15% of rain days account for 50% of the rainfall, 25 to 30% of rain days account for 75% of the rainfall, and 50% of days with the smallest rain amounts account for only 10% of the total. In semi-arid areas such as northern Kenya, this pattern is even more marked as depicted in Figure 9, which shows that almost half the rainfall events over a 2-year period contributed less than 2% of the total rainfall, and that they had rainfall intensities of less than 5 mm/in. On the other hand, 6% of the storms fell with intensities greater than 25 mm/in (a threshold value above which rainfall may be considered erosive, according to Hudson, 1971), and these storms contributed over 70% of the total rainfall (Edwards et al, 1979).
Figure 7. Linearisation of a statistical distribution. Cumulative probability curve plotted on rectangular coordinates. Source: Ven te Chow (1964).
Figure 7. Linearisation of a statistical distribution. Cumulative probability curve linearized on probability paper. Source: Ven te Chow (1964).
Figure 8. June maximum daily rainfall in Lagos, 1915-1926.
Figure 9. Frequency distribution of rainfall intensity at Gatab, northern Kenya.
Most of the record falls of rain are associated with intense tropical cyclones. Figure 10 shows the world's highest recorded rainfall. The totals recorded at Cilaos (Reunion) were the result of an intense tropical cyclone in 1952, which was funnelled up a steep valley rising to 3000 m (Lockwood 1972). The previous world record for 24 hours was also due to the combination of tropical cyclone and land relief. On that occasion, the maximum rainfall occurred at Baguis in the Philippines following the passage of a typhoon in 1911. Less intense, but still remarkable falls of rain commented upon by Jackson (1977) are also shown on the graph.
Rainfall maxima such as those in Figure 10 only give an idea of the expected magnitude of the highest falls, with very long recurrence intervals. For general design purposes, statements about amount, duration and frequency of rainfall are required in order to compare the risk of failure of spillways, culverts and bridges against economic criteria. Such analyses can also be applied to soil erosion problems.
For a given duration, rainfall events can be ranked in either a partial duration series or an extreme value series. Thus, for daily rainfall, events can be selected so that their magnitudes are greater than a certain base value, or the maximum rainfall in any year can be chosen. Either series can be plotted on probability paper to yield recurrence intervals or return periods for a given magnitude. The difference between the two series is that the partial duration series may include several events which occur close together in 1 year. For practical purposes, the two series do not differ much, except in the values of low magnitude (Ven te Chow, 1964). An example of the annual maximum series for four stations in Tanzania is given in Figure 11. These graphs were drawn to assess the return periods of storms which caused landslides in the Uluguru Mountains in Tanzania.
Alternatively, where information from recording rain gauges is available, rainfall intensity can be plotted against duration, and intensity-duration frequency curves can be constructed for different return periods.
Figure 10. The world's highest recorded rainfall and other remarkable falls.
On inselbergs and mountain masses within the tropics, the summits are frequently covered in cloud in locations where the orographic uplift of moist air is sufficient to cause condensation. If the upper slopes are covered in forest, the surfaces of the leaves and branches of trees act as collectors for condensed water vapour. This phenomenon is referred to as occult precipitation, because it does not relate to any rain-making process in the cloud itself and rain gauges placed outside the forest area will not record any rainfall.
In southern and southwest Africa, Marloth (1904) and Nagel (1962) have shown that mist condensation or occult precipitation may contribute between 40 and 94% of the total precipitation on high ground. More recently, Edwards et al (1979) made some preliminary measurements on Mt. Kulal in northern Kenya and concluded that occult precipitation could be a significant addition to the groundwater store.
This mechanism may be important as a contribution to groundwater recharge and as a means of sustaining perennial basal springs on mountains in semi-arid areas. On the other hand, high rates of evaporation of intercepted water, and the deeper rooting zone of trees compared to shorter vegetation, may mean that any additional infiltrated water from occult precipitation will be rapidly used up by the trees.
Persistent and subjective reports of springs drying up following deforestation, and flowing again following reafforestation, point to the value of investigating the detailed water balance of mountains in semi-arid areas. Unfortunately, the water balances are likely to be complex, with both infiltration capacities and rates of input of precipitation varying between forested and non-forested areas. Evaporation and transpiration rates are also likely to differ significantly and, because these components would need to be measured directly, projects aiming to achieve detailed water balances would require careful instrumentation.
Figure 11. Return periods for maximum daily rainfalls in Tanzania.
In many areas, however, summit forests are threatened by fire and by encroachment of grazing lands. If occult precipitation is a significant additional input to the water balance, it becomes increasingly important to conserve these forests. Further research into the survival of basal springs is of major importance in pastoral areas.
